Graph theory proof-diameter/degree relationship

Hi, all!

Here's the problem I've been working on.

Suppose G is connected and suppose every $\displaystyle x \in V(G)$ satisfies $\displaystyle \delta (x) \geq \fraq{(v-1)/2}$.Show that G has diameter no greater than 2.

Where $\displaystyle \delta (x)$ is the degree of a vertex.

So, it shouldn't be hard, but I can't seem to get what the relationship between the degree of a vertex of a graph and its diameter is.

Any help would be greatly appreciated!

Thanks!